It’s once, twice, three times for Bloomberg! Just as The Post suggested, Mayor Bloomberg plans to announce Thursday that he’ll seek to change the city’s term-limits law so he can run for a third term and steer the Big Apple through the fiscal crisis.

Bloomberg also wants more leverage to preserve a key legacy of his tenure: mayoral control of the schools, sources said.

The schools law expires next June and some have already called for it to be weakened.

“The fact that Mike would seek to re-up is very encouraging,” said Meryl Tisch, a member of the state Board of Regents who backs mayoral control.

“The results speak for themselves. The reorganization has yielded real benefits to the school system. Mike used his authority in a reasonable and responsible way.”

The Post first reported yesterday on the push for “Mike The III” in a story today revealing that chief term-limits supporter Ron Lauder had decided to back another four years for Bloomberg and that the mayor had told aides he intended to go for it.

If he pulls it off, Bloomberg would become only the fourth mayor to serve three terms in the last century – following in the footsteps of Fiorello La Guardia, Robert Wagner and Ed Koch.

Bloomberg got a huge boost when Lauder – who bankrolled the 1993 voter initiative that imposed term limits – told The Post today he endorsed temporarily extending the limits to 12 years from eight.

The changes, which would affect all citywide officeholders, borough president and City Council members, will be undertaken by a revision to the 15-year-old city law, not through a public referendum, sources said.

Sources said Bloomberg will announce tomorrow that he wants to run because of his concerns for the city’s welfare amid the meltdown in the New York-dominated financial services industry.

Bloomberg is a former Wall Street trader and founder of the successful financial services firm in his name – and he has a vote of confidence from the city’s business community .

But Bloomberg, who in the past opposed and took action to block changes to term limits, will face a big fight. “That would be abhorrent. That is making an end run around what the voters have done twice,” said Chris Keeley of Common Cause.